The invention is based on an anti-skid brake system as generally defined hereinafter. From U.S. Pat. No. 4,033,637, an anti-skid brake system is known in which a Brake pressure modulation valve assembly, a pressure fluid receiving reservoir and a recirculating pump are associated with a first brake circuit. A floating piston assembly is associated with a second brake circuit. The floating piston assembly includes two cylinders, a pressure modulation piston acted upon by the brake pressure of the first brake circuit for modulating the brake pressure in the wheel brakes of the second brake circuit, a barrier valve controlled by the pressure modulation piston, and a safety piston which in the event of failure of the first brake circuit keeps the pressure modulation piston in its basic position and thereby keeps the barrier valve open. During braking in which there is no danger of skidding, both pistons remain in their basic positions. As a result, if an anti-skid situation occurs after a relatively long period of inactivity, the pressure modulation piston may remain stuck in its position for lowering brake pressure. To make it possible, despite this, to supply brake pressure from the master cylinder to the wheel brakes of the second brake circuit, a safety valve embodied as an overpressure valve is disposed in a bypass around the blocking valve. In the anti-skid situation, this safety valve is intended to make the greatest possible pressure drop possible between the master cylinder and the wheel brakes. Attaining this object, however, has the disadvantage that in emergency braking, that is, if the blocking valve controlled by the pressure modulation piston is closed, the emergency braking pressure in the wheel brake cylinders is substantially less than the pressure generated in the master cylinder. As a result, in the event of emergency braking a very high master cylinder pressure is necessary, yet it may no longer be possible to generate such high pressure by means of a brake pedal alone.